Q: A ball is thrown downward from the top of a building with an initial speed of $$4\ \text{m/s}. If it $$hits the ground in $$2\ \text{s}$$, what is the height of the building? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$h = v_0$ t + \frac{1}{2} g t^2$ = 4 \times 2 + \frac{1}{2} \times 9.8 \times 2^2$ = 8 + 19.6 = 27.6\ \text{m}$$

Q: An object slides down an incline at constant speed. What is the direction of the sum of all forces acting on the object?

The sum of all forces is zero; the net force is $$\textbf{0}$$

Q: A $$10\ \text{kg}$$ box sits on a flatbed truck. The coefficients of static and kinetic friction are $$\mu_s = 0.4$$ and $$\mu_k = 0.3. $$What is the maximum angle $$\theta$$ the truck can be inclined before the box starts to slide?

$$\theta = \arctan(\mu_s) = \arctan(0.4) \approx 21.8^\circ$$

Q: A $$2\ \text{kg}$$ object moving at $$6\ \text{m/s}$$ comes to a stop in $$4\ \text{m}$$ due to friction. What is the coefficient of kinetic friction $$\mu_k$$? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$\mu_k = \frac{v^2$}{2 g d} = \frac{6^2$}{2 \times 9.8 \times 4} = \frac{36}{78.4} \approx 0.46$$

Q: A student walks $$3\ \text{km}$$ East, then $$4\ \text{km}$$ North. What is the direction (angle from East) of the resultant displacement?

$$\theta = \arctan\left(\frac{4}{3}\right) \approx 53.1^\circ$$ North of East

Question 1

A vector $$	extbf{A}$$ points 5 km North, and a vector $$	extbf{B}$$ points 3 km East. What is the magnitude of the resultant vector $$	extbf{A} + 	extbf{B}$$?

Accepted Answer

$$\sqrt{5^2$ + 3^2$} = \sqrt{34} \approx 5.83 km$$

Question 2

A ball is thrown downward from the top of a building with an initial speed of $$4\ 	ext{m/s}. If it $$hits the ground in $$2\ 	ext{s}$$, what is the height of the building? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = v_0$ t + \frac{1}{2} g t^2$ = 4 	imes 2 + \frac{1}{2} 	imes 9.8 	imes 2^2$ = 8 + 19.6 = 27.6\ 	ext{m}$$

Question 3

Which of the following best describes the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

The acceleration is constant and directed downward, $$a = -g$$

Question 4

A rock is projected horizontally from a $$20\ 	ext{m}$$ high cliff with an initial speed of $$5\ 	ext{m/s}. $$What is the magnitude of its velocity just before it hits the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{v_x^2$ + v_y^2$}$$, where $$v_y = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} \approx 19.8\ 	ext{m/s}$$, so $$v = \sqrt{5^2$ + 19.8^2$} \approx 20.4\ 	ext{m/s}$$

Question 5

An object slides down an incline at constant speed. What is the direction of the sum of all forces acting on the object?

Accepted Answer

The sum of all forces is zero; the net force is $$	extbf{0}$$

Question 6

Two objects are connected as a half-Atwood machine: one object rests on a frictionless table, the other hangs off the edge. How does the tension in the rope compare to the weight of the hanging object?

Accepted Answer

The tension is less than the weight of the hanging object

Question 7

A $$10\ 	ext{kg}$$ box sits on a flatbed truck. The coefficients of static and kinetic friction are $$\mu_s = 0.4$$ and $$\mu_k = 0.3. $$What is the maximum angle $$	heta$$ the truck can be inclined before the box starts to slide?

Accepted Answer

$$	heta = \arctan(\mu_s) = \arctan(0.4) \approx 21.8^\circ$$

Question 8

A car of mass $$m$$ increases its speed from $$10\ 	ext{m/s} to$$ $$20\ 	ext{m/s}. $$How much work is required?

Accepted Answer

$$W = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} m (20^2$ - 10^2$) = \frac{1}{2} m (400 - 100) = 150m$$

Question 9

A $$2\ 	ext{kg}$$ object moving at $$6\ 	ext{m/s}$$ comes to a stop in $$4\ 	ext{m}$$ due to friction. What is the coefficient of kinetic friction $$\mu_k$$? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$\mu_k = \frac{v^2$}{2 g d} = \frac{6^2$}{2 	imes 9.8 	imes 4} = \frac{36}{78.4} \approx 0.46$$

Question 10

A student walks $$3\ 	ext{km}$$ East, then $$4\ 	ext{km}$$ North. What is the direction (angle from East) of the resultant displacement?

Accepted Answer

$$	heta = \arctan\left(\frac{4}{3}ight) \approx 53.1^\circ$$ North of East

Question 11

A projectile is launched from the ground with speed $$v_0 at $$angle $$	heta$$ above the horizontal. What is the total time it spends in the air?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Question 12

If an object’s initial velocity is upward and its acceleration is downward, what happens to its speed?

Accepted Answer

The speed decreases

Question 13

A $$5\ 	ext{kg}$$ object is pulled across a horizontal surface with a force of $$20\ 	ext{N}$$, and the coefficient of kinetic friction is $$0.2. $$What is the acceleration?

Accepted Answer

$$a = \frac{F - f_k}{m}$$, $$f_k = \mu_k m g = 0.2 	imes 5 	imes 9.8 = 9.8\ 	ext{N}$$, so $$a = \frac{20 - 9.8}{5} = 2.04\ 	ext{m/s}^2$$

Question 14

Which of the following is NOT a fundamental SI unit?

Accepted Answer

Newton ($$	ext{N})$$

Question 15

A $$1\ 	ext{kg}$$ object is dropped from rest from a height of $$5\ 	ext{m}. $$What is its speed just before hitting the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 5} = \sqrt{98} \approx 9.9\ 	ext{m/s}$$

Question 16

A $$3\ 	ext{kg}$$ object is moving at $$4\ 	ext{m/s}$$ and is brought to rest by a constant force over $$6\ 	ext{m}. $$What is the magnitude of the force?

Accepted Answer

$$F = \frac{1}{2} m v^2$ / d = \frac{1}{2} 	imes 3 	imes 16 / 6 = 8 / 6 = 1.33\ 	ext{N}$$

Question 17

Which equation best represents the Work-Energy Theorem?

Accepted Answer

$$W_{	ext{net}} = \Delta K = K_f - K_i$$

PH101 Unit Exam #1 Study Notes: Chapters 1-5, 7

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학습 가이드 - 플래시카드